On Generalized Kissing Numbers of Convex Bodies
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908536164843520 |
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| author | Li, Yiming Zong, Chuanming |
| author_facet | Li, Yiming Zong, Chuanming |
| contents | In 1694, Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball. This problem and its higher dimensional generalization have been studied by many mathematicians, including Minkowski, van der Waerden, Hadwiger, Swinnerton-Dyer, Watson, Levenshtein, Odlyzko, Sloane and Musin. In this paper, we introduce and study a further generalization of the kissing numbers for convex bodies and obtain some exact results, in particular for balls in dimensions three, four and eight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Generalized Kissing Numbers of Convex Bodies Li, Yiming Zong, Chuanming Metric Geometry 52C17, 11H31 In 1694, Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball. This problem and its higher dimensional generalization have been studied by many mathematicians, including Minkowski, van der Waerden, Hadwiger, Swinnerton-Dyer, Watson, Levenshtein, Odlyzko, Sloane and Musin. In this paper, we introduce and study a further generalization of the kissing numbers for convex bodies and obtain some exact results, in particular for balls in dimensions three, four and eight. |
| title | On Generalized Kissing Numbers of Convex Bodies |
| topic | Metric Geometry 52C17, 11H31 |
| url | https://arxiv.org/abs/2407.17340 |